# Car in corner -- relative airflow

• John Mcrain
In summary, the article discusses the effects of curved flow and yaw angles on Formula 1 cars during cornering. It explains how the airflow over the car is affected by the lateral and yaw forces generated by the car's motion, and how this can impact the car's performance. The article also includes diagrams to illustrate the concepts and provides a link to a more in-depth explanation. Overall, the article aims to shed light on the challenges of replicating curved flow conditions in wind tunnels for car design.

#### John Mcrain

http://mccabism.blogspot.com/2017/08/curved-flow-and-arrows-a3.html

"The nose skirts on the Lotus 80 and Arrows A3 would have suffered from the fact that a Formula 1 car has to generate its downforce in a state of yaw. Thus, in a cornering condition, a car is subjected to a curved flow-field. This is difficult to replicate in a wind-tunnel, hence a venturi tunnel design which worked well in a straight-ahead wind-tunnel condition could have failed dramatically under curved flow conditions. To understand this better, a short digression on curved flow and yaw angles is in order.

The first point to note is that a car follows a curved trajectory through a corner, hence if we switch to a reference frame in which the car is fixed but the air is moving, then the air has to follow a curved trajectory. If we freeze the relative motion mid-corner, with the car pointing at a tangent to the curve, then the air at the front of the car will be coming from approximately the direction of the inside front-wheel, while the air at the back of the car will be coming from an outer direction.

That's the simplest way of thinking about it, but there's a further subtlety. The negotiate a corner, a car generates: (i) a lateral force towards the centre of the corner's radius of curvature; and (ii) a yaw moment about its vertical axis.

Imagine the two extremes of motion where only one of these eventualities occur. In the first case, the car would continue pointing straight ahead, but would follow a curved path around the corner, exiting at right-angles to its direction of travel. In the second case, it would spin around its vertical axis while its centre-of-mass continued to travel in a straight line.

In the first case, the lateral component of the car's velocity vector corresponds to a lateral component in the airflow over the car. The angle which the airflow vector subtends to the longitudinal axis of the car, is the same along the length of the vehicle.
In the second case, the spinning motion also induces an additional component to the airflow over the car. It's a solid body spinning about its centre of mass with a fixed angular velocity, and the tangential velocity of that spin induces an additional component to the airflow velocity along the length of the car. However, the further away a point is from the axis of rotation, the greater the tangential velocity; such points have to sweep out circles of greater circumference than points closer to the centre of mass, hence their tangential velocity is greater.

Now imagine the two types of motion combined. The result is depicted above, in the left-part of the diagram. The white arrows depict the component of the airflow due to 'side-slip': the car's instantaneous velocity vector subtends a small angle to the direction in which its longitudinal axis is pointing. In the reference frame in which the car is fixed, this corresponds to a lateral component in the direction of the airflow which is constant along on the length of the car.
When the yaw moment of the car is included (indicated by the curved blue arrow about the centre-of-mass), it induces an additional airflow component, indicated by the green arrows. Two things should be noted: (i) the green arrows at the front of the car point in the opposite direction from the green arrows at the rear; and (ii) the magnitude of the green arrows increases with distance from the centre of mass. The front of the car is rotating towards the inside of the corner, while the rear of the car is rotating away, hence the difference in the direction of the green arrows. And, as we explained above, the tangential velocity increases with distance from the axis of rotation, hence the increase in the magnitude of the green arrows.
The net result, indicated by the red arrows, is that the yaw-angle of the airflow has a different sign at the front and rear of the car, and the magnitude of the yaw angle increases with distance from the centre-of-mass. (The red arrows in the diagram are pointing in the direction in which the car is travelling; the airflow direction is obtained by reversing these arrows)."

I don't understand above explanation,can you help me.
What white arrow represent,lateral component of velocity?

*In circle exist only tangential velocity which cause tangential airflow and car is at small angle to the direction of travel,due to relative airflow coming from side.

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Lnewqban said:
Only for low speed tight corners, there is a pronounced yaw of the chassis.
The trajectories of front and rear tires have different radii.

You could see additional explanation in the article referred in the above schematic:
http://www.f1-forecast.com/pdf/F1-Files/Honda/F1-SP2_20e.pdf

View attachment 267158
If drive car in right turn in way that place rear-right tyer at road line.Looking at acckerman geometry front-right tyer will be left to the road line due to greater radius.
But now seems that car center line is angled out(yaw out) of turn,so side relative airflow will hit right side of car.

It si opposite as text explain,why my logic don't hold?
Can you explain with geometry why car has some yaw angle into turn if front tyers travel at greater radius then rear tyers?

John Mcrain said:
But now seems that car center line is angled out(yaw out) of turn,so side relative airflow will hit right side of car.
The car is not a point particle. Different parts of it can experience different airflow when it's rotating (yaw). Imagine a long stick tangential to a small circle that the center of the stick moves along.

Lnewqban
A.T. said:
The car is not a point particle. Different parts of it can experience different airflow when it's rotating (yaw). Imagine a long stick tangential to a small circle that the center of the stick moves along.

I don understand this part in my text where author try to explain with two induced flow:
I understand induced flow from yam moment,but don't understand induced flow from "lateral velocity"

"The negotiate a corner, a car generates: (i) a lateral force towards the centre of the corner's radius of curvature; and (ii) a yaw moment about its vertical axis.

Imagine the two extremes of motion where only one of these eventualities occur. In the first case, the car would continue pointing straight ahead, but would follow a curved path around the corner, exiting at right-angles to its direction of travel. In the second case, it would spin around its vertical axis while its centre-of-mass continued to travel in a straight line.

In the first case, the lateral component of the car's velocity vector corresponds to a lateral component in the airflow over the car. The angle which the airflow vector subtends to the longitudinal axis of the car, is the same along the length of the vehicle. "

In circle motion don't exist lateral velocity only tangential velocity
Can you make it clear text above?

John Mcrain said:
If drive car in right turn in way that place rear-right tyer at road line.Looking at acckerman geometry front-right tyer will be left to the road line due to greater radius.
But now seems that car center line is angled out(yaw out) of turn,so side relative airflow will hit right side of car.

It si opposite as text explain,why my logic don't hold?
Can you explain with geometry why car has some yaw angle into turn if front tyers travel at greater radius then rear tyers?
I know my schematic shows a right-hand turn, but that was the best I could find.
Let's keep the car turning left only, like in the schematic.

It seems to me that they are trying to make a regular straight wind tunnel work for a circular airflow situation.
For that, they would need to test a race car with curved shape.
Since they have neither of those, they use vector addition.

"The white arrows depict the component of the airflow due to 'side-slip'."
They know that this specific car has a tendency to over-steer in tight fast curves.
That means that the chassis fishtails some.
Unlike the car that you have described above, the rear tires of this race car do not follow the geometric trajectory of the turn, but skid out or away from the geometric center of rotation.

That characteristic creates an additional angle between the incoming airflow and the longitudinal axis of the car.
Imagine that the rear axle was out of alignment (rotated clockwise a few degrees): folowing a straight trajectory, the car would be crabbing, facing higher aerodynamic drag from its entire right side while its left side would be somehow shielded from incoming airflow.

Now, they need to rotate that curved car in the wind tunnel a few degrees to the left, in order to replicate that side-slip.
The direction in which each point of the car "feels" that airsteam coming from should be like represented by the red arrows of your schematic.
Note that the red arrow by the nose of the car is closer to the tangent of the geometric trajectory than the red arrow by the tail of the car.

Lnewqban said:
I know my schematic shows a right-hand turn, but that was the best I could find.
Let's keep the car turning left only, like in the schematic.

It seems to me that they are trying to make a regular straight wind tunnel work for a circular airflow situation.
For that, they would need to test a race car with curved shape.
Since they have neither of those, they use vector addition.

"The white arrows depict the component of the airflow due to 'side-slip'."
They know that this specific car has a tendency to over-steer in tight fast curves.
That means that the chassis fishtails some.
Unlike the car that you have described above, the rear tires of this race car do not follow the geometric trajectory of the turn, but skid out or away from the geometric center of rotation.

That characteristic creates an additional angle between the incoming airflow and the longitudinal axis of the car.
Imagine that the rear axle was out of alignment (rotated clockwise a few degrees): folowing a straight trajectory, the car would be crabbing, facing higher aerodynamic drag from its entire right side while its left side would be somehow shielded from incoming airflow.

Now, they need to rotate that curved car in the wind tunnel a few degrees to the left, in order to replicate that side-slip.
The direction in which each point of the car "feels" that airsteam coming from should be like represented by the red arrows of your schematic.
Note that the red arrow by the nose of the car is closer to the tangent of the geometric trajectory than the red arrow by the tail of the car.

View attachment 267177

View attachment 267178

"Imagine the two extremes of motion where only one of these eventualities occur. In the first case, the car would continue pointing straight ahead, but would follow a curved path around the corner, exiting at right-angles to its direction of travel.
In the first case, the lateral component of the car's velocity vector corresponds to a lateral component in the airflow over the car. The angle which the airflow vector subtends to the longitudinal axis of the car, is the same along the length of the vehicle. "

What is lateral velocity in circle motion,I don't understand above text?

A.T. said:
The car is not a point particle. Different parts of it can experience different airflow when it's rotating (yaw). Imagine a long stick tangential to a small circle that the center of the stick moves along.
I don't understand basic geometry concept in relation to relative wind.
Any point you choose at car and draw tengent to the local radius,wind hit left side of car except small part behind rear axel.
How then wind produce force which help car go in curve??

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John Mcrain said:
... What is lateral velocity in circle motion,I don't understand above text?
Above text does not make sense to me either.

John Mcrain said:
I don't understand basic geometry concept in relation to relative wind.
Any point you choose at car and draw tengent to the local radius,wind hit left side of car except small part behind rear axel.
How then wind produce force which help car go in curve??
“The red arrows in the diagram are pointing in the direction in which the car is travelling; the airflow direction is obtained by reversing these arrows.”

Please, see reasons some cars don’t enjoy neutral steering:
https://en.m.wikipedia.org/wiki/Understeer_and_oversteer

https://en.m.wikipedia.org/wiki/Slip_angle

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Lnewqban said:
“The red arrows in the diagram are pointing in the direction in which the car is travelling; the airflow direction is obtained by reversing these arrows.”
In my picture at post #8 red line represent local relative airflow

John Mcrain said:
In my picture at post #8 red line represent local relative airflow
Please, note that your schematic is correct for rear axle being aligned with radius of geometric curve and center of curve.
The schematic of the article has located the rear axle rearwards and assumes the car turning respect to the center of mass of the car (tangential velocity of CM is perfectly perpendicular with center of curve).

Besides the introduced angle of skid, the tail of the car is fishtailing respect to the geometric trajectory enough to make direction of airflow come from right direction.

Lnewqban said:
Please, note that your schematic is correct for rear axle being aligned with radius of geometric curve and center of curve.
The schematic of the article has located the rear axle rearwards and assumes the car turning respect to the center of mass of the car (tangential velocity of CM is perfectly perpendicular with center of curve).

Besides the introduced angle of skid, the tail of the car is fishtailing respect to the geometric trajectory enough to make direction of airflow come from right direction.
Yes but this is how it works, radius of curve is allways aligned with rear axel.

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John Mcrain said:
Yes but this is how it works, radius of curve is allways aligned with rear axel.
I agree with you.

Lnewqban said:
I agree with you.
So we still don't know where comes from so much angle which will rotate car to the left into turn and shift relative airflow to hit right side.(from my picture #8)
It is very confusing.

It is.
I believe their assumption may be incorrect.

Race cars don't use Ackermann steering, since during a high g turn, the outside tire has more downforce than the inside, so the outside tire can use more steering angle than the inside.

The yaw on a race car is due to rotational flex and slippage at the contact patches. F1 tires are designed for about 3.5° yaw at maximum load. The similar CART cars of the 1990's when running on high speed ovals, were stiffer still, with 2.5° degree yaw (called working slip angle). F1 cars use skidboards, and underbody tunneling is not allowed. The former CART and current Indy cars do allow underbody tunneling.

F1 races cars have suspension setup for some oversteer in slow turns (the rear end is relatively stiffer than the front), but the aerodynamic downforce is set up for for understeer (rear end has relatively higher downforce) to prevent snap oversteer in high speed turns. These are adjusted depending on the cornering speeds at track. The fastest is Suzuka with one turn taken at around 190 mph. 1990's CART cars were running 220+ mph in the turns, reaching 265 mph top speed on straights just before turns at California speedway during qualifying, and Paul Tracy recorded a trap speed of 255 mph during a Michigan 500 race.

Lnewqban and John Mcrain
Lnewqban said:
It is.
I believe their assumption may be incorrect.
Hi Lnewqban
I think I find answer ,key is slip angle.
Slip angle shift center of turn and now airflow comes from outside at fin shark,producing aerodynamic force into turn ,helps car to drive in corner with even faster speed!
Do you agree whit my drawing?

https://drivetribe.com/p/how-do-f1-shark-fins-work-Ii0ryvnJTLOCsH0kvdK5ew?iid=bBgqpEXCTnS0_XLLDcOH6w

Lnewqban
rcgldr said:
Race cars don't use Ackermann steering, since during a high g turn, the outside tire has more downforce than the inside, so the outside tire can use more steering angle than the inside.

*How find center of turn in anti-acckerman if radius of curve of outside front tyer don't intersect at same turn center?
*Front outside tyer has allways higher vertical load then inner in corner,that implies allways use anti-ackerman?
*Why in video at 3:55 say "it will decrease slip angle of inner tyer" if inner tyer has less load.Isnt less load mean less slip angle?

John Mcrain said:
Hi Lnewqban
I think I find answer ,key is slip angle.
Slip angle shift center of turn and now airflow comes from outside at fin shark,producing aerodynamic force into turn ,helps car to drive in corner with even faster speed!
Do you agree whit my drawing?
I like your drawing and agree with it.